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<b>let </b><font color="Maroon" title="c3">X</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">f</font> being  <a href="partfun1.html#NM1" title="PARTFUN1:NM.1">PartFunc</a> of  <a href="numbers.html#K2" title="NUMBERS:func.2">COMPLEX</a> , <a href="numbers.html#K2" title="NUMBERS:func.2">COMPLEX</a>   st <font color="Olive" title="b1">f</font> <a href="cfdiff_1.html#R2" title="CFDIFF_1:pred.2">is_differentiable_on</a> <font color="Maroon" title="c3">X</font> holds <br/><font color="Maroon" title="c3">X</font> is   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <a href="numbers.html#K2" title="NUMBERS:func.2">COMPLEX</a> </span><br/><b>let </b><font color="Maroon" title="c4">f</font> be   <a href="partfun1.html#NM1" title="PARTFUN1:NM.1">PartFunc</a> of  <a href="numbers.html#K2" title="NUMBERS:func.2">COMPLEX</a> , <a href="numbers.html#K2" title="NUMBERS:func.2">COMPLEX</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c4">f</font> <a href="cfdiff_1.html#R2" title="CFDIFF_1:pred.2">is_differentiable_on</a> <font color="Maroon" title="c3">X</font> implies <font color="Maroon" title="c3">X</font> is   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <a href="numbers.html#K2" title="NUMBERS:func.2">COMPLEX</a>  )</span><br/>



<b>assume </b><a NAME="E1:33"/>
<font color="Maroon" title="c4">f</font> <a href="cfdiff_1.html#R2" title="CFDIFF_1:pred.2">is_differentiable_on</a> <font color="Maroon" title="c3">X</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c3">X</font> is   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <a href="numbers.html#K2" title="NUMBERS:func.2">COMPLEX</a> </span><br/>

<a NAME="E2:33"/><b>then </b>
<font color="Maroon" title="c3">X</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <font color="Maroon" title="c4">f</font>
 
<b>by </b><i><a class="ref" href="cfdiff_1.html#D9" target="_self" title="CFDIFF_1:def.9">Def9</a></i>;<br/>
<b>hence </b><a NAME="E3:33"/>
<font color="Maroon" title="c3">X</font> is   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <a href="numbers.html#K2" title="NUMBERS:func.2">COMPLEX</a> 
 <b>by </b><i><a class="ref" href="xboole_1.html#T1" title="XBOOLE_1:th.1">XBOOLE_1:1</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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